A Noise-robust and Overshoot-free Alternative to Unsharp Masking for Enhancing the Acuity of MR Images

Abstract

Poor acutance of images (unsharpness) is one of the major concerns in magnetic resonance imaging (MRI). MRI-based diagnosis and clinical interventions become difficult due to the vague textural information and weak morphological margins on images. A novel image sharpening algorithm named as maximum local variation-based unsharp masking (MLVUM) to address the issue of ‘unsharpness’ in MRI is proposed in this paper. In the MLVUM, the sharpened image is the algebraic sum of the input image and the product of the user-defined scale and the difference between the output of a newly designed nonlinear spatial filter named maximum local variation-controlled edge smoothing Gaussian filter (MLVESGF) and the input image, weighted by the normalised MLV. The MLVESGF is a locally adaptive 2D Gaussian edge smoothing kernel whose standard deviation is directly proportional to the local value of the normalized MLV. The values of the acutance-to-noise ratio (ANR) and absolute mean brightness error (AMBE) shown by the MLVUM on 100 MRI slices are 0.6463 ± 0.1852 and 0.3323 ± 0.2200, respectively. Compared to 17 state-of-the-art image sharpening algorithms, the MLVUM exhibited a higher ANR and lower AMBE. The MLVUM selectively enhances the sharpness of edges in the MR images without amplifying the background noise without altering the mean brightness level.

Introduction

The Relevance of the Sharpening Algorithms in MRI Studies

Poor acutance of images is one of the major concerns in magnetic resonance imaging (MRI). The term ‘unsharpness’ is often used in medical imaging to reflect low acutance. The issue of unsharpness is more severe in low-field MRI than in high-filed MRI. Among various sequences of MRI, certain images from sequences have relatively high unsharpness. For example, fluid-attenuated inversion recovery (FLAIR) sequence images are sharper compared to the images of the fast spin echo (FSE) sequence. Certain anomalies like glioblastoma multiforma always have vague and uncertain margins on MRI. Because of weak edges, it is difficult to contour such lesions during radiation treatment/image-guided surgical planning. Edge-based segmentation schemes like the active contour model are often used for segmenting structures from MRI [1]. Edge-based segmentation schemes will perform efficiently only if the structures are separated by well-defined margins. The textural information on magnetic resonance (MR) images is extensively used nowadays for the diagnosis of a broad spectrum of diseases like small vessel disease [2], Alzheimer’s disease [3], and ischemic stroke lesions [4]. The textural features will be apparent only if the images are sharper. Hence, the techniques for resolving the unsharpness in MRI have great significance in medical imaging.

There have been certain attempts to design special reconstruction techniques and acquisition sequences that are useful to produce edge-enhanced MR images. The edge-enhanced spatio-temporal constrained reconstruction (STCR) [5] and edge-enhancing gradient echo sequence [6] are two examples of such special reconstruction techniques and acquisition sequences. However, it is difficult to design a generic reconstruction technique or acquisition sequence that can produce MR slices with high edge quality. In this paradigm, post-processing algorithms can be effectively used to enhance the edge strength in the MR slices. Super-resolution reconstruction (SRR) algorithms are extensively used nowadays to produce high-resolution MR images. Certain SRR algorithms produce reconstructions with blurred edges. Sharpening/deblurring algorithms are used to improve the edge quality in super-resolution MRI reconstructions [7].

Review of Existing Image Sharpening Algorithms

Terms like ‘textural enhancement’, ‘edge enhancement’, ‘enhancement of contextual information’, and ‘local contrast enhancement’ are also used in literature to describe ‘image sharpening’. The shock filter (SF) [8] and unsharp masking (UM) [9, 10] are the most popular among the image sharpening algorithms. In the shock filter, sharpened form ‘$Y$’ of the input image is obtained using (1) [8],

$$Y=X+\lambda {\mathrm{\nabla }}_X\left[s,g,n,\left(X,,\ast ,,\ast ,H_L\right)\right]$$ 1

The variable ‘$X$’ in (1) represents the input image. The variable ‘${\mathrm{\nabla }}_X$’ represents a two-dimensional array of local gradient magnitude values within the input image ‘X’. The mathematical operator ‘**’ symbolizes two-dimensional convolution. The mask ‘$H_L$’ that is convolved with input image is a discrete Laplacian kernel. The variable ‘λ’ is generally called as scale. It is an arbitrary/user-defined parameter. The value of the scale decides the sharpening effect. The more is the value of the scale, the sharper will be the output image.

The unsharp masking involves multiple steps. The first step of the unsharp masking algorithm is the separation of the high-frequency content from the input image. The difference between the input image and its smoothed version gives the high-frequency content. The smoothing operation yields detail (low-frequency content) of the input image. Often a traditional two-dimensional Gaussian filter is employed to extract the detail. The low-frequency component is estimated by smoothing the input image with a 2D Gaussian kernel. Whole above steps in separating the high-frequency content is mathematically expressed in (2) [9, 10].

$$D=X-(X\ast \ast H_G)$$ 2

In (2), the Gaussian filter ‘H_G’ convolved with the input image ‘$\mathrm{X}$’ yields the detail. Difference between the input image and the detail ‘$(\mathrm{X}\ast \ast {\mathrm{H}}_{\mathrm{G}})$’ yields the high frequency content ‘$\mathrm{D}$’. In the second step of the unsharp masking, the high-frequency content separated from the input image obtained in (2) undergoes a thresholding operation as written in (3) [9, 10],

$${\mathrm{D}}_{\mathrm{T}}\left(\mathrm{m},\mathrm{n}\right)=\left\{\begin{array}{c}\mathrm{D}\left(\mathrm{m},\mathrm{n}\right)\hfill \\ 0\hfill \end{array}\right)\begin{array}{c}\mathrm{if}\left|\mathrm{D},\left(\mathrm{m},,,\mathrm{n}\right)\right|\ge \mathrm{T}\hfill \\ \mathrm{Otherwise}\hfill \end{array}\mathrm{m}=1,2,3\cdots \cdots \mathrm{M}\&\mathrm{n}=1,2,3,\cdots \cdots \mathrm{N}$$ 3

In the thresholding step, relatively weaker high-frequency components are excluded. If the magnitude of local value of the difference ‘$|\mathrm{D}(\mathrm{m},\mathrm{n})|$’ is greater than an arbitrary level ‘$\mathrm{T}$’, the value ‘$\mathrm{D}(\mathrm{m},\mathrm{n})$’ is transferred to ‘${\mathrm{D}}_{\mathrm{T}}(\mathrm{m},\mathrm{n})$’, without any change. The value of ‘${\mathrm{D}}_{\mathrm{T}}(\mathrm{m},\mathrm{n})$’ is made zero if the difference ‘$|\mathrm{D}(\mathrm{m},\mathrm{n})|$’ is less than the level. The pixels at which the difference ‘$|\mathrm{D}(\mathrm{m},\mathrm{n})|$’ is less than the level is considered as non-edge or noise-affected pixels. The pixels at which the difference ‘$|\mathrm{D}(\mathrm{m},\mathrm{n})|$’ is greater than the level is considered as edge pixels. The thresholding operation is expected to avoid noise amplification. The level, ‘T’, is computed from the highest value among the absolute values in the array ‘D’ as expressed in (4) [9, 10].

$$T=amax\left\{\left|D\right|\right\},0\le a\le 1$$ 4

The arbitrary parameter ‘α’ in (4) scale down the level ‘$\mathrm{T}$’. The parameter ‘α’ is generally called as ‘threshold’. In the third step of the unsharp masking, the sharpened output is obtained from (5) [9, 10].

$$Y=X+\lambda D_T$$ 5

The arbitrary parameter, ‘λ’ in (5) is called as scale. It decides the effect of the sharpening operation.

Dynamic unsharp masking (DUM) [11] is an extension of the traditional UM [9, 10]. In DUM [11], the product of the corresponding elements in the adjusted two-dimensional array of the scale values and the difference of the original image and detail component obtained via low-pass filtering is added back to the original image for getting the sharpness enhanced image. The sharpened output of DUM [11],

$$\begin{array}{cc}\hfill Y\left(m,,,n\right)=& X\left(m,,,n\right)+W\left(m,,,n\right)\left(X,\left(m,,,n\right),-,X_{\mathit{LP}},\left(m,,,n\right)\right),\hfill \\ \hfill & m=1,2,\cdots \cdots ,M\mathrm{and}n=1,2,\cdots \cdots ,N\hfill \end{array}$$ 6

In (6), ‘$X$’ is the input image, ‘$W$’ is the adjusted two-dimensional array of the scale values, and ‘$X_{\mathit{LP}}$’ is the low-pass filtered version of the input image. A neighbourhood averaging filter with window size 5 × 5 is used as the low-pass filter. The variables ‘$M$’ and ‘$N$’ denote the number of rows and the columns in the input image, respectively. The adjusted weight, ‘$W\left(m,,,n\right)$’ corresponding to a pixel, ‘$X\left(m,,,n\right)$’ is computed from a user-defined scale value, the standard deviation of pixels within a window of dimension 11 × 11 around the contextual pixel ‘$X\left(m,,,n\right)$’, mean of pixel values within the window, and the global mean of the input image as in (7) [11].

$$\begin{array}{cc}\hfill W\left(m,,,n\right)=& \alpha \left[{\mu }_X,/,\mu ,\left(m,,,n\right),+,log,(\sigma \left(m,,,n\right))\right],\hfill \\ \hfill & m=1,2,\cdots \cdots ,M\mathrm{and}n=1,2,\cdots \cdots ,N\hfill \end{array}$$ 7

In (7), ‘$\alpha$’ is a user-defined scale value, ‘${\mu }_X$’ is the global mean of the pixel intensities in the input image, ‘$\mu \left(m,,,n\right)$’ is the mean value of the pixels within the window around the contextual pixel ‘$X\left(m,,,n\right)$’, and ‘$\sigma \left(m,,,n\right)$’ is the standard deviation of pixels within the window.

The adaptive bilateral filter (ABF) [12] and quadratic weighted median filter-based edge enhancement (QWMFEE) algorithm [13] are techniques that emerged from the image denoising filters. In the ABF [12], the weighting function in the traditional bilateral filter is modified by adding a locally adaptive offset term. In QWMFEE [13], a fraction of the difference between the quadratic weighted median filter (QWMF) outputs obtained from the input image and its negative is added to the input image to produce the edge-enhanced image. The QWMF is a weighted median extension of the two-dimensional Teager filter proposed by Thurnhofer and Mitra [14]. Adaptive shock filter (ASF) [15] is a combination of the shock filter and forward diffusion. The weight of the shock filter is adjusted dynamically in proportion to the local gradients. The forward diffusion is also an image denoising algorithm.

The fuzzy-contextual contrast enhancement (FCCE) algorithm [16] and dominant orientation-based texture histogram equalization (DOTHE) [17] are two image sharpening techniques based on the concept of the conventional histogram equalization. In the first step of the FCCE algorithm [16], a homogeneity fuzzy sub-set (HFS) is computed based on the fuzzy similarity of every pixel in the image with their 8-connected neighbours. In the second step, a fuzzy complement of the HFS is computed. The fuzzy complement of HFS is known as texture fuzzy sub-set (TFS). In the third step, a histogram of values in the TFS is constructed. This histogram is known as fuzzy textural histogram (FTH). A tentative or intermediate output is obtained by applying the traditional histogram equalization on the FTH. The refined output image is computed as weighted sum of the intermediate output and the input image. The weights are obtained from the HFS. In the DOTHE [17], the input image is divided into patches. The variance of pixels within each patch is computed. Similarly, the patch is represented with the help of singular values using singular value decomposition (SVD). Then, the patches are classified into textured and nontextured categories based on the variance of pixel values and the singular values along dominant orientation. Following this, a histogram is constructed by counting the number of occurrences of the pixel values exclusively from the dominant-orientation/textured patches. Then, the enhanced grey level values are computed from the cumulative histogram, as done in the traditional histogram equalization.

Certain sharpening algorithms are based on morphological (binary operations). Morphological image enhancement (MIE) [18–21] and multiscale bowler-hat transform [22] belong to this category. In the MIE, the sharpened image is the difference between the sum of the input image and the output of the top-hat transform and the output of the bottom-hat transform. The top-hat filter operates in two steps. In the first step, a morphological opening operation is applied on the input image. In the second step, the result of morphological opening is subtracted from the input image. Similarly, in the bottom-hat filter also has two steps. In the first step, the input image is subjected to a morphological closing operation. In the second step, the input image is subtracted from the result of morphological closing. In the first step of the MBHT, a set of finite number of ‘opened images’ are produced by applying morphological opening on the input image, using disc-shaped structuring elements with different radius. In the second step, another set comprising the same number of ‘opened images’ are produced by applying morphological opening on the input image, using linear structuring elements with different lengths. The operation, ‘morphological open’ has two stages. In the first stage, the input is subjected to an erosion operation. In the second stage, the eroded image is subjected to a dilation operation. For both erosion and dilation, the same structuring elements are used. In the third step of the MBHT, the absolute difference between the corresponding opened images produced using disc-shaped and linear structuring elements are computed. The pixel value at any arbitrary location in the output of MBHT is the highest value of the absolute difference between the opened images produced using disc-shaped and linear structuring elements corresponding to that location.

Sharpening algorithms like nonlinear amplification of spatial derivative (NASD) [23, 24] and nimble filter (NF) [25] are based on the concept of amplifying the spatial derivatives. In the NASD algorithm [23, 24], the pixel value in the sharpened image at any arbitrary location is formulated as a function of amplified values of the directional derivatives along all eight directions at that location. To accomplish robustness to noise (to avoid noise amplification), the directional gradients are amplified nonlinearly in proportion to the mean of their absolute values. For obtaining the sharpened image ‘$Y$’, a spatially adaptive-kernel ‘$H_S$’ shown in (8) is convolved with the input image ‘$X$’ [23, 24]. A pixel value ‘$Y(m,n)$’ in the sharpened image is [23, 24]

$$\mathrm{Y}\left(\mathrm{m},,,\mathrm{n}\right)={\mathrm{H}}_{\mathrm{s}}**{\theta }_{\mathrm{x}\left(\mathrm{m},,,\mathrm{n}\right)}\mathrm{given}{\mathrm{H}}_{\mathrm{s}}=\left[\begin{array}{c}\frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\\ \frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\\ \frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\end{array},\begin{array}{c}\frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\\ \frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\\ \frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\end{array},\begin{array}{c}\frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\\ \frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\\ \frac{1-\mathrm{k}(\mathrm{m},\mathrm{n})}{8}\end{array}\right],\mathrm{k}(\mathrm{m},\mathrm{n})>1$$ 8

In (8), ‘${\mathrm{\Theta }}_{X(m,n)}$’ indicates the eight-connected neighbourhood of the pixel ‘$X(m,n)$’. Using a non-linear function, ‘$\mathrm{\Psi }[Z\left(m,,,n\right)]$’ mean of the absolute values of directional gradients and ‘$Z\left(m,,,n\right)$’ is mapped into [0 1] as given in (9) [23, 24]. In the NASD, the amplification of spatial gradient (in effect the sharpness of the output image) is controlled via a user-defined parameter, acuity control parameter (ACP). To avoid noise amplification, the value of ACP is adjusted locally in proportion to the non-linear function ‘$\mathrm{\Psi }[Z\left(m,,,n\right)]$’ as given in (10) [23, 24]. The non-linear function penalizes the ACP at non-edge pixels.

$$\begin{array}{cc}& \psi \left[Z,\left(\mathrm{m},\mathrm{n}\right)\right]=\left[1,-,e^{-\left(\frac{z\left(\mathrm{m},\mathrm{n}\right)}{\zeta }\right)}\right],\mathrm{given}Z\left(\mathrm{m},,,\mathrm{n}\right)\hfill \\ \hfill & =\frac{1}{8}\sum _{i=-1}^{+1}\sum _{j=-1}^{+1}\left|X,\left(\mathrm{m}+\mathrm{i},\mathrm{n}+\mathrm{j}\right),-,X,\left(\mathrm{m},,,\mathrm{n}\right)\right|\hfill \end{array}$$ 9

$$k\left(m,,,n\right)=1+K\mathrm{\Psi }\left[Z,\left(m,,,n\right)\right],K>1and0\le \mathrm{\Psi }\left[Z,\left(m,,,n\right)\right]\le 1$$ 10

In (9), ‘$\mathrm{K}$’ is the global value of ACP. The variable ‘ζ’ is another arbitrary operational parameter of the NASD algorithm, named ‘noise suppression parameter (NSP)’.

The principle of the NF [25] is similar to that of the NASD [23, 24]. In the NF, the value of an arbitrary pixel ‘$Y\left(m,,,n\right)$’ in the sharpened image [25],

$$\begin{array}{cc}\hfill Y\left(m,,,n\right)=& \eta X\left(m,,,n\right)+\left(1,-,\eta \right)\hfill \\ \hfill & \left(\frac{X\left(m,-,1,,,n\right)+X\left(m,+,1,,,n\right)+X\left(m,,,n,-,1\right)+X\left(m,,,n,+,1\right)}{4}\right),\hfill \end{array}$$

$$m=1,2,\cdots \cdots ,M\mathrm{and}n=1,2,\cdots \cdots ,N\mathrm{Given}\eta >1$$ 11

In (11), ‘$X$’ is the input image. The variables, ‘$M$’ and ‘$N$’ denote numbers of rows and columns in the image. The variable ‘$\eta$’ denotes the scale that determines the amount of enhancement. The operation in (11) can be realized with the help of convolution as [25]

$$Y=\left[\begin{array}{c}0\\ {}^{\left(1,-,\eta \right)}{/}_4\\ 0\end{array},\begin{array}{c}{}^{\left(1,-,\eta \right)}{/}_4\\ \eta \\ {}^{\left(1,-,\eta \right)}{/}_4\end{array},\begin{array}{c}0\\ {}^{\left(1,-,\eta \right)}{/}_4\\ 0\end{array}\right]**X$$ 12

Content-adaptive image detail enhancement (CIDE) [26] is another sharpening algorithm based on the principle of amplifying the spatial gradients. Unlike the NASD [23, 24] and the NF [25], the CIDE [26] is meant for enhancing fine details in the images. In the CIDE algorithm [26], fine details are amplified by selectively magnifying gradients in the whole input image, except those at the edge’s pixels. The enhancement is formulated as a L₀-norm-based global optimization problem.

Adaptive power-law transformation (APLT) [27], local contrast enhancement transform (LCET) [28–31], local contrast enhancement (LCE) algorithm [32], and local S-curve transformation (LST) [33] belong to the category of local contrast enhancement. The APLT [27] is a locally adaptive gamma transformation in which the natural logarithm of reciprocal of the dynamic range of pixels within a window of arbitrary size around the contextual pixel is used as the local value of exponent (gamma). APLT is performed on normalized images in the range 0–1. The enhanced image in LCET [28–31] is

$$\begin{array}{cc}\hfill Y\left(m,,,n\right)=& \left(\frac{k\vartheta }{\sigma \left(m,,,n\right)+b}\right)\left(X,\left(m,,,n\right),-,c,\mu ,\left(m,,,n\right)\right)+{\left(\mu ,\left(m,,,n\right)\right)}^a,\hfill \\ \hfill & m=1,2\cdots M\&n=1,2\cdots N\hfill \end{array}$$ 13

In (13), ‘$X\left(m,,,n\right)$’ is an arbitrary pixel value in the input image and ‘$Y\left(m,,,n\right)$’ is the corresponding pixel value in the enhanced image. The variable ‘$\vartheta$’ indicates the global mean of pixel intensities. The variables ‘$\mu (m,n)$’ and ‘$\sigma \left(m,,,n\right)$’ respectively indicate the mean and standard deviation of pixel intensities in the neighbourhood of the contextual pixel ‘$X\left(m,,,n\right)$’. The variables K, a, b, and c are user-defined parameters.

In LCE [32], the ratio of the pixels value and the mean of neighbourhood values within a window of 5 × 5 size around it is computed at each pixel location where the pixel value and the local mean are greater than a user-defined threshold. The user-defined threshold is suggested as equal to one [32]. The ratio after a log transformation is mapped to a range 0-L-1 to produce the sharpened/enhanced image. An arbitrary pixel in the enhanced image at (m,n), m = 1,2,….M and n = 1,2,….N [32],

$$Y\left(m,,,n\right)=\left\{\begin{array}{cc}\log (X\left(m,,,n\right)/{\mu }_X(m,n))& X\left(m,,,n\right)>\theta \&{\mu }_X(m,n)>\theta \\ 0& \mathrm{Otherwise}\end{array}\right)$$ 14

In (14), ‘$\theta$’ is a user-defined threshold whose value is suggested as one. ‘${\mu }_X(m,n)$’ is the mean value of the pixels in a neighbourhood of 5 × 5, around $\left(m,,,n\right)$, and ‘$X$’ is the input image.

The LST [33] is a contrast transformation algorithm. In the first step, the input image is partitioned into non-overlapping blocks. LST is applied to the block after normalising the grey level to a range [0 1]. The transformed grey levels are mapped back to the actual dynamic range of the grey levels within the block. In the LST, the turning points of the S-transform are set manually.

Limitations of the Existing Image Sharpening Algorithms

No mechanism is available in the shock filter [8] to avoid amplification of noise. The Gaussian smoothing kernel used in the unsharp masking [9, 10] is a linear filter. The weights in the kernel depend only on the spatial distance from the centre. The Gaussian kernel has the same smoothing response on noise-affected pixels and edges. Hence, it cannot be expected that the difference of the input and Gaussian smoothed images may have higher values at the edge pixels than those at non-edge or noisy pixels. It is difficult to distinguish the noise-affected pixels and the edge pixels from the difference of the input and Gaussian smoothed images via the thresholding operation. Thresholding is a mathematical function with jump discontinuity. The thresholding process introduces sharp discontinuities in the output images of the unsharp masking. In UM, when the threshold is too low, noise is amplified uncontrollably. The unsharp masking over-enhances the contrast at the edges causing haloes and overshoot artefact. A halo is a bright region or line that appears in the sharpened image at the regions corresponding to the high contrast regions in the input image. When the value of the threshold is very high (close to one), the unsharp masking will not have any significant impact. The DUM [11] amplifies the background noise.

The ABF [12] also has the issue of noise amplification. Up to a certain extent, the issue of noise amplification can be addressed by increasing the value of the radiometric parameter. However, no mechanism is available in the ABF to control the improvement in sharpness. The QWMF [14], which forms the base of the QWMFEE [13], is generally used for suppressing impulse noise. In MRI, the noise is Rician at low SNR and addictive Gaussian at high SNR. In QWMFEE [13], the pixel intensities move to two extremes of the grey level range. The QWMFEE [13] causes intensity saturation and intolerably disturb the brightness characteristics of the input image. Such drastic change in brightness characteristics is not permissible while enhancing medical images as the brightness features carry diagnostically meaningful information. The ASF [15] over-smooth homogenous regions of the input image. Fine details are often lost in the output images, and the ASF causes cartoon artefacts.

No mechanism is available in the FCCE [16] algorithm to control the improvement in sharpness. The FCCE algorithm [16] increases the mean brightness level considerably. The output images produced by the FCCE algorithm [16] will be significantly greater than the input images. In the DOTHE [17], two pixels with the same intensity, one lying in a homogenous patch and another lying in a textured patch, will be enhanced equally. Contrast at homogenous regions should not be enhanced as far as an ideal sharpening scheme is concerned. Even though the number of occurrences of the pixel values from only textured patches is considered for computing the histogram, certain pixel values still may have significantly high histogram amplitude, causing contrast overshoot at that pixel value. The DOTHE [17] does not have brightness-preserving characteristics. Often the output images will be considerably brighter compared to the input images.

The MIE [18–21] spoils the natural appearance of images. Sharpened images are relatively darker than input images. It introduces processing-induced artefacts and amplifies noise. As a series of morphological opening operations are involved in the MBHT [22], it is computationally heavy. The natural appearance of the output of MBHT [22] is spoiled by the processing-induced artefacts. Mean brightness and textural features are intolerably disturbed. Output images look considerably darker than the input images.

The NASD [23, 24] is also susceptible to haloes and overshoot artefacts. The NF filter [25] does not sharpen the diagonal edges. As the scale in the NF is constant and not dynamically adaptive to local pixel statistics, it amplifies noise. The CIDE [26] amplifies noise intolerably and introduces processing-induced artefacts. CIDE is not meant for sharpening edges; rather, it is meant for amplifying fine details in the images. The APLT [27] saturates the image, and the pixel values get polarized at lower and upper extrema of the dynamic range. The APLT does not have brightness-preserving features. It spoils the natural appearance of images. The LCET [28–31] has five user-defined parameters, including the radius of the window. As there are numerous user-defined/arbitrary operational parameters in the LCET, it is difficult to adjust them simultaneously. The LCET produces output images that have a washed-out appearance. The LCET does not sharpen the edges. The output produced by LCE [32] is often significantly different from the input image. Information is lost intolerably. Fixing the turning points in LST [33] manually is tedious. As LST operates on non-overlapping blocks, it introduces blockiness or blocky artefacts.

Research Objectives, Novelty and Highlights

Objectives: A novel image sharpening algorithm named maximum local variation-based unsharp masking (MLVUM) to address the issue of ‘unsharpness’ in MRI is proposed in this paper.

Novelty: (i) The MLVUM is built on a newly designed maximum local variation-controlled edge smoothing Gaussian filter (MLVESGF). (ii) A maximum local variation-based weighting scheme is employed in the MLVUM to restrict the noise amplification.

Highlights: (i) Sharpened images produced by the MLVUM are free from overshoot artefact/intensity saturation, haloes, and discontinuity artefact. (ii) The MLVUM well-preserves the mean brightness level of images. (iii) The MLVUM selectively enhances the sharpness of edges in the MR images without amplifying the background noise.

Organization of the Content

Section 1: The relevance of the sharpening algorithms in MRI studies, a review on existing image sharpening algorithms, limitations of the existing image sharpening algorithms, research objectives, and novelty of the proposed MLVUM have been covered in Sect. 1.

Section 2: The analytical procedure for computing the sharpened image in MLVUM, its working principle, analytical formulations of the objective image quality metrics used for validation and performance assessment, and particulars of the MRI dataset used for its development and validation are discussed in Sect. 2.

Section 3: In Sect. 3, the MLVUM is compared with 17 state-of-the-art image sharpening techniques, both subjectively and quantitatively.

Section 4: The impact of the operational parameters of the MLVUM on the perceived quality of the sharpness enhanced images and the objective image quality metrics are analysed in Sect. 4. Based on the analysis, guidelines regarding the selection of the operational parameters are provided.

Section 5: In Sect. 5, a summary of technical contributions, a summary of observations and inferences, advantages of the MLVUM, its commercial viability/application prospects, design constraints and limitations, and hints for future enhancement are included.

Methodology

Maximum Local Variation-Based Unsharp Masking

Formulation of MLVUM

In the maximum local variation-based unsharp masking (MLVUM), sharpened image, ‘Y’, is the algebraic sum of the input image ‘$X$’ and the product of the scale, ‘λ’, and the difference between the output of the maximum local variation-controlled edge smoothing Gaussian filter (MLVESGF) and the input image, weighted by the normalized MLV.

$$\mathrm{Y}=\mathrm{X}+\lambda \mathrm{D}$$ 15

In (15), the variable, ‘D’, is the difference between the output of the MLVESGF and the input image ‘$X$’, weighted by the normalized MLV ‘$\mathrm{\nabla }$’.

$$\begin{array}{cc}\hfill D\left(m,,,,n\right)=& \left[X,\left(m,,,,n\right),-,F,\left(m,,,,n\right)\right]\mathrm{\nabla }\left(m,,,,n\right),\hfill \\ \hfill & m=1,2\cdots \cdots ,M\&n=1,2\cdots \cdots ,N\hfill \end{array}$$ 16

In (16), ‘F’ is the output of the MLVESGF and ‘∇’ is the two-dimensional array of normalized MLV values. The MLVESGF is a locally-adaptive 2D Gaussian smoothing kernel whose standard deviation is directly proportional to the local value of the normalized MLV. An arbitrary pixel at (m,n), $m=1,2\cdots \cdots ,M\mathit{and}n=1,2\cdots \cdots ,N$, in the output of the MLVESGF is,

$$\begin{array}{cc}\hfill F(m,n)=& \sum _{i=-R}^{+R}\sum _{j=-R}^{+R}{H}_{\mathit{mn}}\left(i,,,j\right)X\left(m,+,i,,,,n,+,j\right),\hfill \\ \hfill & m=1,2\cdots \cdots ,M\&n=1,2\cdots \cdots ,N\hfill \end{array}$$ 17

In (17), the MLVESGF at the pixel location described by (m,n) is

$${H_{\mathit{mn}}\left(i,,,j\right)=e}^{-\left(\frac{i^2+j^2}{2{\left[{\sigma }_{\mathit{mn}}\right]}^2}\right)}/\sum _{i=-R}^{+R}\sum _{j=-R}^{+R}{e}^{-\left(\frac{i^2+j^2}{2{\left[{\sigma }_{\mathit{mn}}\right]}^2}\right)}$$ 18

In (18), the variable ‘R’ indicates the radius of the MLVESGF. For a radius, ‘R’, the kernel is of dimension, [2R + 1] × [2R + 1]. The variable, ‘σ_mn’ indicates the standard deviation of the MLVESGF, ‘H_mn’ at the pixel location described by (m,n). Its value is set as directly proportional to the local value of the normalized MLV. The standard deviation of the MLVESGF at (m,n),

$${\sigma }_{\mathit{mn}}={\sigma }_{\mathit{max}}\left[\mathrm{\nabla },(,m,,,,n,)\right]$$ 19

In (19), ‘${\sigma }_{\max }$’ is a arbitrary/user-defined operational parameter that describes the highest possible value of the standard deviation of the MLVESGF. The MLV at an arbitrary location ‘$(m,n)$’ is the maximum of the absolute difference between the contextual pixel, ‘$X(m,n)$’ and its eight-connected neighbours. The MLV is used as a measure of local ‘unsharpness’. The potential of the MLV to reflect the image sharpness is already evidenced by Bahrami and Kot [34] and Gao et al. [35]. The selection of MLV to characterize the local ‘unsharpness’ is motivated by [34] and [35]. The MLV at an arbitrary location ‘$(m,n)$’ is [34, 35]

$$\begin{array}{cc}\hfill \mathrm{\nabla }(m,n)=& max\{|X(m-1,n-1)-X(m,n)|,\hfill \\ \hfill & |X(m-1,n)-X(m,n)|,\hfill \\ \hfill & |X(m-1,n+1)-X(m,n)|,\hfill \\ \hfill & |X(m,n-1)-X(m,n)|,\hfill \\ \hfill & |X(m,n+1)-X(m,n)|,\hfill \\ \hfill & |X(m+1,n-1)-X(m,n)|,\hfill \\ \hfill & |X(m+1,n)-X(m,n)|,\hfill \\ \hfill & |X(m+1,n+1)-X(m,n)|\}\hfill \end{array}$$ 20

In a subsequent step, the two-dimensional array of the gradient magnitude is normalized to the range [0 1] as

$$\mathrm{\nabla }(m,n)=\frac{\mathrm{\nabla }(m,n)}{max\{\mathrm{\nabla }\}}$$ 21

The schematic of the steps involved in the computation of the sharpened image in MLVUM, described in (15) to (21) is depicted in Fig. 1.

Fig. 1.

Schematic of the steps involved in the computation of the sharpened image in MLVUM

The pseudo-code that demonstrates the computation of sharpened image in the MLVUM is shown below.

Pseudo-code of MLVUM
Step 1:	Initialize the values of user-defined parameters; scale ‘λ’, radius of the MLVESGF ‘$R$’ and highest possible value of the standard deviation of the MLVESGF ‘${\sigma }_{\max }$’
Step 2	Compute two-dimensional array of normalized MLV values ‘$\mathrm{\nabla }$’ using (20) and (21)
Step 3:	Start a raster scan from the first pixel of the image ‘$X\left(m,,,n\right),m=1\mathrm{and}n=1$’ and compute local value of standard deviation of the MLVESGF ‘${\sigma }_{\mathit{mn}}$’ using (19)
Step 4:	Compute MLVESGF ‘$H_{\mathit{mn}}$’ from ‘${\sigma }_{\mathit{mn}}$’ and ‘$R$’ using (18)
Step 5:	Compute the filtered pixel value ‘$F(m,n)$’ using (17) with the help of the kernel ‘$H_{\mathit{mn}}$’
Step 6:	Move through the entire pixels in the input image trough a raster scan and repeat the steps 3 to 5 to compute the filtered image ‘$F$’
Step 7:	From the output of the MLVESGF ‘$F$’, input image ‘$X$’ and normalized MLV ‘$\mathrm{\nabla }$’, compute the weighted difference ‘$D$’ using (16)
Step 8:	From the input image ‘$X$’, weighted difference ‘$D$’ and scale ‘λ’ compute the sharpened image ‘$Y$’ using (15)

Working of the MLVUM

The normalized value of MLV ‘$\mathrm{\nabla }(m,n)$’ at edge pixels will be relatively higher compared to that at noise-affected pixels. According to (19), the standard deviation of the MLVESGF ‘σ_mn’ will be relatively high at edge pixels. As per (17) and (18), edge pixels will undergo a relatively higher level of smoothing. In effect, the MLVESGF selectively smooths the edges. Consequently, the magnitude of the difference between the input image and the output of the MLVESGF, ‘$X\left(m,,,n\right)-F\left(m,,,n\right)$’ in (16) will be relatively higher at edge pixels. When the difference ‘$X\left(m,,,n\right)-F\left(m,,,n\right)$’ is further weighted by the normalized MLV, ‘$\mathrm{\nabla }(\mathrm{m},\mathrm{n})$’ the weighted difference between the input image and the output of the MLVESGF, ‘$D\left(m,,,n\right)$’, in (16), will have considerable magnitude only at the edge pixels. When the product of the user-defined scale value and the weighted difference between the input image and the output of the MLVESGF is added to the input image as in (15), the edges in the input image will be sharpened selectively.

Objective Metrics Used for Performance Assesment of the MLVUM

Image quality metrics useful for assessing the quality of sharpened images are rare. Recently, Simi et al. [23] has demonstrated a highly-reliable approach for assessing the quality of sharpened images. An ideal image sharpening algorithm should selectively sharpen the edges in the input image without magnifying the noise content and without altering the mean brightness level. Hence, two objective quality metrics are used to evaluate the performance of the MLVUM. They are absolute mean brightness error (AMBE) and acutance-to-noise ratio (ANR). The AMBE reflects the absolute difference between the mean brightness levels of input and sharpened images [36]. The AMBE can be computed as [36]

$$\mathrm{AMBE}\left(X,,,Y\right)=\left|\left(\frac{1}{\mathit{MN}},\sum _{m=1}^M,\sum _{n=1}^N,X,(m,n)\right),-,\left(\frac{1}{\mathit{MN}},\sum _{m=1}^M,\sum _{n=1}^N,Y,(m,n)\right)\right|$$ 22

In (22), ‘$X$’ is the input image and ‘$Y$’ is the sharpened image. The variables ‘$M$’ and ‘$N$’ respectively indicate the number of rows and number of columns in the image. The ANR is computed from the acutance of the output image ‘$Y$’ and the standard deviation of noise in it. The ANR ‘$\rho$’ is [23]

$$\rho \left(Y\right)=\frac{A(Y)}{{\sigma }_n(Y)}$$ 23

In (23), ‘${\sigma }_n(Y)$’ is the standard deviation of noise in the output image ‘$Y$’ and ‘$A(Y)$’ is the sharpness of edges in it. Following the recommendation in [23], the standard deviation of noise in the output image is estimated using the popular Liu’s noise model [37] and the sharpness of edges in the output image is quantitatively measured with the help of the S₃ sharpness metric [38]. The selection of the S₃ sharpness metric is motivated by the recommendations regarding the quality assessment of sharpened images reported by Krasula et al. [39]. The ability of the S₃ sharpness metric to reflect the acutance of sharpened images and its agreement with perceptual sharpness ratings are evidenced in [39].

Particulars of the MRI Dataset

A well-established MRI dataset already used in the literature for the design and evaluation of image sharpening algorithms [23, 24, 40, 41] is used in this paper. The set specimen images used for the development and validation of the MLVUM are acquired with the help of a 1.5 Tesla 2D MRI scanner manufactured by GE Medical Systems (Model: Signa HDxt), available at Hind Labs, Government Medical College Kottayam, Kerala, India. The series of acquisition is MR spectroscopy. Slice thickness and inter-slice gap set during the image acquisition are 5 mm and 1.5 mm, respectively. Images from T1 fast spin-echo contrast-enhanced (FS-ECE), T2 fluid attenuation inversion recovery (FLAIR), diffusion-weighted imaging (DWI), gradient recalled echo (GRE), and 1000b array spatial sensitivity encoding technique (ASSET) pulse sequences are used [23, 24, 40, 41].

Results

The proposed MLVUM is compared with 17 state-of-the-art image sharpening techniques, both subjectively and quantitatively. The state-of-the-art image sharpening techniques against which the MLVUM is compared are SF [8] UM [9, 10], DUM [11], ABF [12], QWMFEE [13], ASF [15], FCCE [16], DOTHE [17], MIE [18–21], MBHT [22], NASD [23, 24], NF [25], CIDE [26], APLT [27], LCET [28–31], LCE [32, and LST [33].

Subjective/Qualitative Comparison with Existing Image Sharpening Algorithms

Here, the proposed MLVUM is compared against the state-of-the-art image sharpening techniques in terms of the subjective quality of the output images. Aspects like the sharpness of edges, severity of noise amplification, brightness preservation, and processing-induced artefacts are considered for assessing the subjective quality of output images produced by various sharpening algorithms. Because of the space constraints, the pictorial results corresponding to three MR slices are produced in results. Those three representative MR slices are furnished in Fig. 2. The representative MR slices in Fig. 2 belong to the FSE-CE sequence. The issue of the ‘unsharpness’ is more prominent in the FSE-CE sequence than in other sequences of MRI.

Fig. 2.

Three test images. (a) Test image 1. (b) Test image 2. (c) Test image 3

The ABF (Figs. 3a, 4a, and 5a), DUM (Figs. 3f, 4f, and 5f), and SF (Figs. 3p, 4p, and 5p) intolerably amplify noise. Visually annoying pixel intensity variations seen in the homogenous regions of the output images of ABF, DUM, and SF is due to amplified noise. In the output images of the ASF in Figs. 3b, 4b, and 5b, homogenous regions are over-smoothed. Fine details are lost. The ASF causes cartoon artefacts.

Fig. 3.

Output images of various sharpening algorithms corresponding to the test image 1. (a) ABF, (b) ASF, (c) APLT, (d) CIDE, (e) DOTHE, (f) DUM, (g) LCET, (h) LCE, (i) LST, (j) MIE, (k) MBHT, (l) NASD, (m) NF, (n) FCCE, (o) QWMFEE, (p) SF, (q) UM, and (r) MLVUM

Fig. 4.

Output images of various sharpening algorithms corresponding to the test image 2. (a) ABF, (b) ASF, (c) APLT, (d) CIDE, (e) DOTHE, (f) DUM, (g) LCET, (h) LCE, (i) LST, (j) MIE, (k) MBHT, (l) NASD, (m) NF, (n) FCCE, (o) QWMFEE, (p) SF, (q) UM, and (r) MLVUM

Fig. 5.

Output images of various sharpening algorithms corresponding to the test image 3. (a) ABF, (b) ASF, (c) APLT, (d) CIDE, (e) DOTHE, (f) DUM, (g) LCET, (h) LCE, (i) LST, (j) MIE, (k) MBHT, (l) NASD, (m) NF, (n) FCCE, (o) QWMFEE, (p) SF, (q) UM, and (r) MLVUM

The output images of the APLT in Figs. 3c, 4c, and 5c and the output images of the QWMFEE in Figs. 3o, 4o, and 5o are saturated uncontrollably. The pixel values in the output images are polarized at the lower and upper extrema of the dynamic range. The information content is lost considerably. Output images of APLT and QWMFEE look unnatural. In the output images of the CIDE in Figs. 3c, 4c, and 5c, significant improvement in edge strength is not evident. Rather, fine details and noise in the homogenous regions of the input images are amplified uncontrollably. The CIDE does not sharpen the edges, rather; it is meant for amplifying fine details in the images.

Output images of DOTHE (Figs. 3e, 4e, and 5e), LCET (Figs. 3g, 4g, and 5g), NF (Figs. 3m, 4m, and 5m), and FCCE (Figs. 3n, 4n, and 5n) are significantly brighter than the input images. The APLT, QWMFEE, DOTHE, LCET, and NF do not have brightness-preserving features. The mean brightness level of the sharpened images produced by these algorithms is significantly different from that of the input images. Such drastic change in brightness characteristics is not permissible while enhancing medical images as the brightness features carry diagnostically meaningful information. Significant improvement in edge strength is not evident in the output images of the LCET in Figs. 3g, 4g, and 5g. The output images of the LCET have a washed-out appearance. Information content in the output images of LCE in Figs. 3h, 4h, and 5h, is significantly different from that in the input images. Information continent of the images is altered intolerably. The LST operates on non-overlapping blocks, and it introduces blockiness or blocky artefacts, as seen in Figs. 3i, 4i, and 5i.

The natural appearance of the output images of MIE (Figs. 3j, 4j, and 5j) and MBHT (Figs. 3k, 4k, and 5k) is spoiled by processing-induced artefacts. Sharpened images are relatively darker than input images. Amplified noise is visible in the output images of both MIE and MBHT. Mean brightness level and textural features are intolerably disturbed.

Haloes and overshot artefacts can be observed in the output images of the NASD (Figs. 3l, 4l, and 5l) and UM (Figs. 3q, 4q, and 5q). The bright regions visible in the sharpened images corresponding to the high-contrast regions in the input images are haloes. In the output images of the MLVUM in Figs. 3r, 4r, and 5r, the sharpness of edges has improved significantly. Noise is not amplified. The mean brightness levels of the output images are very close to that of the corresponding input images in Fig. 2. In terms of the subjective quality of the sharpened images assessed with respect to sharpness of edges, noise amplification, brightness preservation, and processing-induced artefacts, the MLVUM is observed to be superior to 17 state-of-the-art image sharpening algorithms, namely, SF [8] UM [9, 10], DUM [11], ABF [12], QWMFEE [13], ASF [15], FCCE [16], DOTHE [17], MIE [18–21], MBHT [22], NASD [23, 24], NF [25], CIDE [26], APLT [27], LCET [28–31], LCE [32], and LST [33].

Objective/Quantitative Comparison with Existing Image Sharpening Algorithms

The values of the ANR and AMBE estimated from the output images of various sharpening algorithms are shown in Tables 1 and 2. Bar graphs of mean values of ANR and AMBE on 100 test images shown by various sharpening algorithms are shown in Fig. 6. A good image sharpening algorithm should enhance the edges without amplifying noise and without altering the mean brightness level. A good image sharpening algorithm should exhibit high ANR and low AMBE. In Table 1 and Fig. 6a, the ABF, SF, and UM exhibit significantly low ANR. The APLT, QWMFEE, and MLVUM have exhibited comparatively higher values of the ANR. In Table 2 and Fig. 6b, the AMBE values shown by APLT and QWMFEE are significantly higher than those shown by the MLVUM. High values of the AMBE shown by APLT and QWMFEE indicate that the mean brightness levels of their output images are significantly different from that of the input images. In Table 2 and Fig. 6b, the values of the AMBE shown by LCET and DOTHE are intolerably high. The LCET and DOTHE do not have brightness-preserving features. Among 18 image sharpening algorithms, the lowest value of AMBE is exhibited by the MLVUM.

Table 1.

ANR estimated from the output images of various sharpening algorithms

Method	Image 1	Image 2	Image 3	Summary on 100 images
ABF	0.0976	0.0861	0.1693	0.1177 ± 0.0451
ASF	0.2846	0.1977	0.5214	0.3346 ± 0.1675
APLT	0.5559	0.5647	1.1629	0.7612 ± 0.3479
CIDE	0.2659	0.2576	0.3210	0.2815 ± 0.0345
DOTHE	0.2796	0.3090	0.3450	0.3112 ± 0.0328
DUM	0.2427	0.1892	0.3060	0.2460 ± 0.0585
LCET	0.4608	0.4301	0.3740	0.4216 ± 0.0440
LCE	0.3435	0.3212	0.3010	0.3219 ± 0.0213
LST	0.4023	0.3615	0.6342	0.4660 ± 0.1471
MIE	0.4005	0.3589	0.5379	0.4324 ± 0.0937
MBHT	0.3369	0.3089	0.3318	0.3259 ± 0.0149
NASD	0.2653	0.2344	0.6138	0.3712 ± 0.2107
NF	0.5111	0.5081	0.5584	0.5259 ± 0.0282
FCCE	0.4284	0.4305	0.4222	0.4270 ± 0.0043
QWMFEE	0.5157	0.5279	1.0934	0.7123 ± 0.3301
SF	0.0787	0.0681	0.1420	0.0963 ± 0.0400
UM	0.1135	0.1034	0.2758	0.1642 ± 0.0968
MLVUM	0.5848	0.4997	0.8544	0.6463 ± 0.1852

Table 2.

Values of the AMBE estimated from the output images of various sharpening algorithms

Method	Image 1	Image 2	Image 3	Summary on 100 images
ABF	0.4090	0.5366	0.1395	0.3617 ± 0.2027
ASF	1.1305	0.8933	0.3307	0.7848 ± 0.4108
APLT	26.2165	27.1271	17.8316	23.7251 ± 5.1242
CIDE	10.1837	8.6338	5.4507	8.0894 ± 2.4130
DOTHE	36.1419	39.1674	31.0059	35.4384 ± 4.1260
DUM	2.7973	5.3081	2.1343	3.4132 ± 1.6742
LCET	31.0586	37.4666	16.1449	28.2234 ± 10.9400
LCE	58.4492	95.7707	73.2265	75.8155 ± 18.7950
LST	1.1194	1.0672	0.1840	0.7902 ± 0.5256
MIE	3.0765	4.9104	1.3355	3.1075 ± 1.7877
MBHT	23.8608	23.4340	6.7728	18.0225 ± 9.7449
NASD	0.6310	0.9546	0.1560	0.5805 ± 0.4017
NF	36.2882	40.4222	19.3429	32.0178 ± 11.1697
FCCE	16.6676	19.0789	17.7829	17.8431 ± 1.2068
QWMFEE	30.5078	32.9755	19.2606	27.5813 ± 7.3108
SF	0.7268	1.3018	0.4324	0.8203 ± 0.4422
UM	2.6211	3.0720	0.2671	1.9867 ± 1.5062
MLVUM	0.3816	0.5235	0.0918	0.3323 ± 0.2200

Fig. 6.

Bar-graphs of mean values of ANR and AMBE on 100 test images shown by various sharpening algorithms. (a) Bar-graph of ANR shown by various sharpening algorithms. (b) Bar-graph of AMBE shown by various sharpening algorithms

The MLVUM exhibited higher values of ANR and lower values of AMBE compared to 17 state-of-the-art image sharpening algorithms. Relatively high values of ANR shown by the MLVUM justify its ability to selectively enhance the edges without amplifying the background noise. Relatively low values of the AMBE exhibited by the MLVUM indicate its ability to preserve the mean brightness level. Both subjective and objective evaluations prove that the proposed MLVUM is superior to 17 state-of-the-art image sharpening algorithms.

Discussions

The influence of the operational parameters of the MLVUM on the perceived quality of the sharpened images and on the objective image quality metrics are analysed here. Based on the analysis, guidelines regarding the selection of the operational parameters are provided. Variations of the S₃ metric against scale for various values of the radius of the MLVESGF on three test images are shown in Fig. 7a-c. On all three test images, the S₃ metric versus scale curves for different values of radius of the MLVESGF are overlapping each other. It indicates that the selection of the radius of the MLVESGF does not have much impact on the improvement in sharpness. The sharpness of output images increases monotonically with scale value. Variations of the standard deviation of noise in the sharpened images against scale for various values of the radius of the MLVESGF on three test images are shown in Fig. 7d-f. It can be seen that at all values of scale, the standard deviation of noise is minimum when the radius of the MLVESGF is low. Variations of the AMBE against scale for various values of the radius of the MLVESGF on three test images are shown in Fig. 7g-i. It can be seen that at all values of scale, AMBE is minimum when the radius of the MLVESGF is low. To avoid noise amplification and to preserve mean brightness level, the radius of the MLVESGF should be low.

Fig. 7.

Variation of image quality statistics with respect to operational parameters of MLVUM. (a) S₃ metric versus scale for test image 1. (b) S₃ metric versus scale for test image 2. (c) S₃ metric versus scale for test image 3. (d) Standard deviation of noise versus scale for test image 1. (e) Standard deviation of noise versus scale for test image 2. (f) Standard deviation of noise versus scale for test image 3. (g) AMBE versus scale for test image 1. (h) AMBE versus scale for test image 2. (i) AMBE versus scale for test image 3

Output images of the MLVUM for various values of radius of the Gaussian kernel and scale corresponding to three test images are shown in Fig. 8. In Fig. 8, regardless of the selection of the radius of the MLVESGF, the mean brightness of the sharpened images is intolerably altered when the scale is equal to or above 10. In Fig. 8a, d and g, the sharpened images look natural and the edges in them are appreciably enhanced irrespective of the selection of the radius of the MLVESGF. A selection of scale value around 5 and the radius of the MLVESGF less than six are observed to be suitable for the MRI dataset used in this study. In the recent design of MLVUM, the user has the freedom to select the scale and radius of the MLVESGF according to the application.

Fig. 8.

Output images of the MLVUM for various values of radius of the Gaussian kernel and scale corresponding to the input image 1. (a) Radius of the Gaussian kernel = 2 and scale = 5. (b) Radius of the Gaussian kernel = 2 and scale = 15. (c) Radius of the Gaussian kernel = 2 and scale = 30. (d) Radius of the Gaussian kernel = 4 and scale = 5. (e) Radius of the Gaussian kernel = 4 and scale = 15. (f) Radius of the Gaussian kernel = 4 and scale = 30. (g) Radius of the Gaussian kernel = 6 and scale = 5. (h) Radius of the Gaussian kernel = 6 and scale = 15. (i) Radius of the Gaussian kernel = 6 and scale = 30

Conclusion

Summary of Technical Contributions: A novel image sharpening algorithm named maximum local variation-based unsharp masking (MLVUM) to address the issue of ‘unsharpness’ in MRI was proposed in this paper.

Summary of Observations and Inferences: The MLVUM exhibited higher values of acutance-to-noise ratio and lower values of AMBE compared to 17 state-of-the-art image sharpening algorithms. Relatively high values of ANR shown by the MLVUM justify its ability to selectively enhance the edges without amplifying the background noise. Relatively low values of the AMBE exhibited by the MLVUM indicate its ability to preserve the mean brightness level.

Advantages of MLVUM: (i) Sharpened images produced by the MLVUM are free from overshoot artefact/intensity saturation, haloes and discontinuity artefact. (ii) The MLVUM well-preserves the mean brightness level of images. (iii) The MLVUM selectively enhances the sharpness of edges in the MR images without amplifying the background noise.

Application Prospects/Commercial Viability of MLVUM: The proposed MLVUM can be used to enhance the textural information and edges in MR images. Prior sharpening of edges will be helpful to improve the efficiency of edge-based segmentation algorithms used for localizing structures on MRI. The MLVM can improve the accuracy of the diagnostic decision in automated frameworks that use textural features for the diagnosis of diseases like small vessel disease, Alzheimer's disease, and ischemic stroke lesions.

Future Scope

Directions for Future Enhancement: (i) The scalability of MLVUM needs to be tested on other medical imaging modalities and natural-scene images. (ii) There is an urgent need for objective metrics that can reflect the perceptual quality of sharpened images. (iii) Optimization techniques can be employed to automate the parameter selection process of MLVUM.

Author Contribution

Dr. Damodar Reddy Edla (first author and supervisor): resources, data curation, supervision, and project administration. Simi V.R. (corresponding author): conceptualization, software, investigation, and writing (original draft). Dr. Justin Joseph (third author): methodology, validation, formal analysis.

Availability of Data and Material

Data may be provided on request.

Code Availability

Code can be made available on request.

Declarations

Ethics Approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Consent to Participate

Not applicable.

Consent for Publication

Not applicable.

Conflict of Interest

The authors declare no competing interests.